Question

point A B and C are collinear on AC and AB:BC = 3/4. A is located at (x,y), B is located at (4,1) and C is located at (12,5). what are the values of x and y?

Answer 1

Answer:

x = -2 and y = -2

Step-by-step explanation:

The expression for calculating the point that divides the coordinate of two endpoints A(x, y) and B (x₁, y₁) in the ratio a:b with point C(X, Y) on the line is as shown below;

$B$$(X, Y) =$ $(\dfrac{ax_1+bx}{b+a}, \dfrac{ay_1+by}{b+a})$

Given B(X, Y) = (4, 1), C(x₁, y₁) = (12,5) and AB:BC = a:b = 3/4

From the given coordinates, X = 4, Y = 1, x₁ = 12 y₁ = 5, a = 3 and b =4

From the coordinates above;

$X = \dfrac{ax_1+bx}{b+a}$

$4 = \dfrac{3(12)+4x}{4+3}\\\\4 = \dfrac{36+4x}{7}\\\\\\4*7 = 36+4x\\28 = 36+4x\\28-36 = 4x\\-8 = 4x\\x = -8/4\\x= -2$

Similarly to get y;

$1 = \dfrac{3(5)+4y}{4+3}\\\\1 = \dfrac{15+4y}{7}\\\\\\1*7 = 15+4y\\7 = 15+4y\\7-15 = 4y\\-8 = 4y\\y= -8/4\\y= -2$

Hence the value of x is -2 and y is -2.